In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).

Using elements from the theory of ergodic backward stochastic differential equations (BSDE), we study the behavior of forward entropic risk measures. We provide their general representation results (via both BSDE and convex duality) and examine their behavior for risk positions of long...

Multi-dimensional backward stochastic Riccati differential equations (BSRDEs in short) are studied. A closed property for solutions of BSRDEs with respect to their coefficients is stated and is proved for general BSRDEs, which is used to obtain the existence of a global adapted solution to some...